LONDON — The Daily Mail apologized to Melania Trump on Wednesday and agreed to pay damages to settle two lawsuits she filed over an article last year asserting that the professional modeling agency she worked for in the 1990s had also been an escort service.

“We accept that these allegations about Mrs. Trump are not true and we retract and withdraw them,” a lawyer for the British newspaper told a judge, Andrew Nicol, at the Royal Courts of Justice in London. “We apologize to Mrs. Trump for any distress that our publication caused her. To settle Mrs. Trump’s two lawsuits against us, we have agreed to pay her damages and costs.”

The terms of the settlement were not immediately disclosed. She had sought compensatory and punitive damages of at least $150 million, according to the filing.

The Daily Mail published its article on Mrs. Trump on Aug. 20, 2016, quoting from a report in a magazine in Slovenia, where she was born, and a biography of her by a journalist, Bojan Pozar.

In September, Mrs. Trump sued The Daily Mail in Montgomery County, Md., and in London, and the tabloid quickly published a retraction.

After the Maryland court dismissed that case, saying it did not have jurisdiction, Mrs. Trump filed a new case in February, in New York.

Her new lawsuit did not explicitly mention the White House or President Trump or even her status as the wife of a presidential candidate at the time the article was published.

Instead, it said that the article had harmed her opportunities “to launch a broad-based commercial brand in multiple product categories,” noting that “the plaintiff is one of the most photographed women in the world,” and asserting that “the plaintiff’s brand has lost significant value.”

On Jan. 20, the day Mr. Trump was sworn in as president, the White House altered its online biography of Mrs. Trump, after complaints that the original wording promoted her line of jewelry.

Mr. Trump has faced criticism that his business dealings around the world have created conflicts of interest in his official role, and he has put his adult sons in charge of his holdings rather than sell them or put them into a blind trust.

Mrs. Trump also sued a Maryland blogger, Webster Tarpley, who published claims like those cited by The Daily Mail and agreed to pay a settlement.

The Daily Mail released what it called a joint statement on Wednesday describing the apology and the settlement. Charles J. Harder, a lawyer for Mrs. Trump, did not respond immediately on Wednesday to requests for comment.